login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of combinatorially inequivalent cyclic subgroups of S_n of order 6. Number of partitions of n of order 6.
4

%I #14 May 23 2020 13:34:14

%S 1,2,3,5,7,9,12,16,19,24,29,34,40,48,54,63,72,81,91,104,114,128,142,

%T 156,171,190,205,225,245,265,286,312,333,360,387,414,442,476,504,539,

%U 574,609,645,688,724,768,812,856,901,954,999,1053,1107,1161,1216,1280

%N Number of combinatorially inequivalent cyclic subgroups of S_n of order 6. Number of partitions of n of order 6.

%C Two permutation groups are combinatorially equivalent iff they have the same cycle index. Order of partition is lcm of its parts.

%H Alois P. Heinz, <a href="/A074752/b074752.txt">Table of n, a(n) for n = 5..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,2,-1,-1,0,1,1,-1).

%F G.f.: x^5*(1+x-x^6)/((x-1)*(x^2-1)*(x^3-1)*(x^6-1)). More generally, g.f. for number of partitions of order d is Sum_{i divides d} mu(d/i)*1/Product_{j divides i} (1-x^j).

%t LinearRecurrence[{1,1,0,-1,-1,2,-1,-1,0,1,1,-1},{1,2,3,5,7,9,12,16,19,24,29,34},60] (* _Harvey P. Dale_, May 23 2020 *)

%Y Column k=6 of A256067, A256554.

%K easy,nonn

%O 5,2

%A _Vladeta Jovovic_, Sep 28 2002